Stability and absolute stability of a general 2-D non-linear FM second model

Author(s): Q. Zhu and G.-D. Hu
DOI: 10.1049/iet-cta.2009.0624

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Author(s): Q. Zhu ¹ and G.-D. Hu ¹
- Affiliations: 1: Department of Electronics and Information Engineering, School of Information Engineering, University of Science and Technology Beijing, Beijing, People's Republic of China
Source: Volume 5, Issue 1, 6 January 2011, p. 239 – 246
DOI: 10.1049/iet-cta.2009.0624 , Print ISSN 1751-8644, Online ISSN 1751-8652

This study deals with the stability and absolute stability of the general 2-D non-linear time-invariant Fornasini–Marchesini (FM) second model. At first, a Lyapunov-type stability theorem is presented to sufficiently guarantee the stability and (globally) asymptotical stability of general 2-D non-linear FM second model. Then, for the globally asymptotical stability, it is further improved to lessen the conservatism of the stability theorem. More importantly, the improved theorem can derive global stability criteria which have the form of linear matrix inequalities. Furthermore, based on the two theorems, some absolute stability criteria are obtained for 2-D FM second model with sector-bounded non-linearity. Finally, three numerical examples show the advantage of the improved stability theorem.

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Stability and absolute stability of a general 2-D non-linear FM second model

Stability and absolute stability of a general 2-D non-linear FM second model

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